The Scientific Work of Jorgen Lund and a Personal Assessment of its Significance

A selection of the more important works of Jorgen Lund, are described. The industrial features of the periods in which specific developments in rotordynamics took place are discussed, together with these developments themselves and the investigators who made them. Lund’s contributions are included within the latter part of this framework. The comparative value of Lund’s work is considered in terms of several criteria, which are judged to apply to the work of investigators generally. These criteria are used to examine the characteristics of three important pioneers of vibration technology, to demonstrate the validity of these criteria. Lund’s contributions are shown to be of high caliber when judged by the same criteria.

Stochastic Analysis of a Fractionally Damped Beam

This paper presents a general analytical technique for stochastic analysis of a continuous beam whose damping characteristic is described using a fractional derivative model. In this formulation, the normal-mode approach is used to reduce the differential equation of a fractionally damped continuous beam into a set of infinite equations each of which describes the dynamics of a fractionally damped spring-mass-damper system. A Laplace transform technique is used to obtain the fractional Green’s function and a Duhamel integral type expression for the system’s response. The response expression contains two parts, namely zero state and zero input. For a stochastic analysis, the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic characteristics of the system. Closed form stochastic response expressions are obtained for White noise. The approach can be extended to all those systems for which the existence of normal modes is guaranteed.

An Adding Mass Method for Stiffly Mechanical System Simulation and Applications to Construction Machinery

A characteristic improvement method for dynamic simulation of a stiff mechanical system by adding mass is presented. Hydraulic systems with check valves and control valves on construction machinery exhibit piecewise-linear characteristics for hydraulic flow rate and spool stroke. The proposed improvement method involves no time delay in determining the mass by considering both eigenvalue distortion of the system and time response. This paper shows a practical application to the boom derricking system of a rough terrain crane, and demonstrates that this method is useful for dynamic simulation of hydraulic system including stiff piecewise-linear elements.

Basin of Attraction of the Simplest Walking Model

Passive dynamic walking is an important development for walking robots, supplying natural, energy-efficient motions. In practice, the cyclic gait of passive dynamic prototypes appears to be stable, only for small disturbances. Therefore, in this paper we research the basin of attraction of the cyclic walking motion for the simplest walking model. Furthermore, we present a general method for deriving the equations of motion and impact equations for the analysis of multibody systems, as in walking models. Application of the cell mapping method shows the basin of attraction to be a small, thin area. It is shown that the basin of attraction is not directly related to the stability of the cyclic motion.

Utilization of Coupled Simulation in the Fatigue Loads Prediction of a Hydraulically Driven Log Crane

Welded structures, such as hydraulically driven booms, are disposed to fatigue damage. Design against fatigue requires information on the fatigue resistance of a structure’s critical details and the fatigue loads that act on each detail. The present paper introduces a method based on dynamic simulation for determining the fatigue loads in a hydraulically driven log crane. The detailed simulation model was built up in the MBS-software environment in which the flexible mechanism model and the equations describing the hydraulic system were combined. The complete simulation model was verified by comparing measurements to numerical results. This comparison shows that there is a clear correspondence between the simulated and measured results. It was thus shown that it is possible to create a simulation model which can be used realistically for determining stresses in fatigue analysis. The model was employed in the study of the fatigue loads, which are formed when the crane is being loaded.

Experimental and Analytical Investigation on Spaghetti Problem

The dynamic behavior of the flexible beam, which is pulled into the slit of the elastic wall with a constant velocity, is discussed with multibody dynamics formulation and experiments. The vibration of the free tip of a flexible beam increases rapidly as pulling into the slit, and this behavior is called “Spaghetti Problem”. The effect of gap size of the slit on the behavior of Spaghetti Problem is especially focused. Dynamic behavior of the beam is simulated numerically and examined the accuracy of the presented formulation by changing the gap size and the pulling velocity of the beam as parameters. It is clarified that the presented modeling method simulates the experimental results quite well, and the gap size and the pulling velocity influence the increase of the lateral vibration near the inlet of the slit.

Experimental Validation of a Dynamic Model for Flexible Link Mechanisms

This paper presents an experimental validation of a finite element approach for the dynamic analysis of flexible multi-body planar mechanisms. The mathematical model employed accounts for mechanism geometric and inertial non-linearities and considers coupling effects among rigid-body and elastic motion. A flexible five-bar linkage actuated by two electric motors is employed as a test case. Experimentally determined link absolute deformations are compared with the numerical results obtained simulating the system dynamic behavior through the mathematical model. The experimental and numerical results are in good agreement especially after the very first transient period.

Bayesian Estimation of Cumulative Damage From Seismic Response Records of Buildings

This paper discusses the estimation of probability distributions of damage using response records from instrumented buildings subjected to seismic excitations. The objective of the paper is to show how the information on the evolution of the mechanical properties of a system can be used to assess the state of cumulative damage. This implies expressing damage on the structural members in terms of its influence on the residual mechanical properties of the system. The information on the inelastic behavior from response records is used in a bayesian formulation along with a damage function to update prior probability distributions of damage. The damage function models the hysteretic cycles of inelastic response in terms of an initial damage and of the displacement amplitudes of the response cycles. It describes the evolution of the secant stiffness through the cycles of inelastic response as a function of cumulative damage and displacement amplitudes. The updating of probability distributions of damage for single degree of freedom systems is presented first. Extensions to the case of non-linear multi-degree of freedom systems are discussed next. Examples of reinforced concrete frames are given for illustrative purposes.

Reduction of Arbitrary Dynamical Systems by Wavelet Bases

A procedure is developed for the identification and classification of nonlinear and time-varying dynamical systems based on measurements of their input and output. The procedure consists of reducing the governing equations with respect to a basis of scaling functions. Given the localizing properties of wavelets, the reduced system is well adapted to predicting local changes in time as well as changes that are localized to particular components of the system. The reduction process relies on traditional Galerkin techniques and recent analytical expressions for evaluating the inner product between scaling functions and their derivatives. Examples from a variety of dynamical systems are used to demonstrate the scope and limitations of the proposed method.

Optimal Sensor and Actuator Configuration for Structural Identification

A methodology is presented for designing cost-effective optimal sensor and actuator configurations useful for structural model updating and health monitoring purposes. The optimal sensor and actuator configuration is selected such that the resulting measured data are most informative about the condition of the structure. This selection is based on an information entropy measure of the uncertainty in the model parameter estimates obtained using a statistical system identification methodology. The optimal sensor and actuator configuration is selected as the one that minimizes the information entropy. A discrete optimization problem arises which is solved efficiently using genetic algorithms. This study also addresses important issues related to robustness of the optimal sensor and actuator configuration to unavoidable uncertainties in the structural model, as well as issues related to the optimal sensor and actuator configurations designed to monitor multiple damage scenarios. The theoretical developments are illustrated by designing the optimal configuration for a 40-DOF two-dimensional truss structure subjected to an impulse hammer excitation.